Integer Sequences

For a fixed integer n, let x1, x2, ..., x2n be a sequence that contains each of the 2n different n bit integers exactly once. To be precise, we say an integer is an n bit integer if it can be expressed in binary with exactly n bits (with, perhaps, some leading zeros). We say the sequence is gradual if two consecutive numbers differ in exactly one bit when written in binary and the first and last n